Melissa F. Koenen ^1,2,3 Romée Geelen ^1,2,3 Marleen Balvert ^1,2,3 Hein Fleuren ^1,2,3*

• ¹ Tilburg University, Tilburg, Netherlands
• ² School of Economics and Management, Tilburg University, Tilburg, Netherlands
• ³ Zero Hunger Lab, Tilburg University, Tilburg, Netherlands

Optimization techniques, such as linear programming, can be used to estimate the minimum cost of a nutrient-adequate food basket, to determine if individuals or households can afford nutritious diets. These cost estimates typically account for seasonal fluctuations but often overlook significant disruptions in the availability of affordable nutritious food that can severely impact food and nutrition security.This paper proposes a tree-based method, the binary search tree, to assess the resilience of the cost estimate of the minimum-cost food basket. In particular, this method aims to identify indispensable foods in these baskets -those whose unavailability would lead to a substantial cost increase. The binary search tree operates by iteratively excluding essential food items while ensuring the construction of minimum-cost nutritious baskets. It considers all relevant combinations of foods up to a specified size and avoids unnecessary optimizations, thereby saving computation time. We describe how the resulting tree can be evaluated and condensed to capture only the necessary information for decision makers. The construction and evaluation of the binary search tree are independent of the (dietary) restrictions or type of optimization model (i.e., linear, non-linear or integer) included.In general, the binary search tree can identify all (combinations of) foods whose exclusion leads to a significant cost increase of a nutritious food basket. Furthermore, it can detect possible substitute effects between foods and identify key limiting nutrients. A case study is presented in which the binary search tree is applied to data from Ebonyi, Nigeria, modeled using linear programming. We report all combinations of up to five foods that, when unavailable, can impact food and nutrition security in Ebonyi.The BST can provide insights into local food and nutrition security when facing drastic disruptions in access to nutritious foods by identifying indispensable foods. Its results can be used to inform and design interventions in the context of humanitarian operations.